How to Find the Circumcenter
The circumcircle of a triangle is the circle that contains the vertices of the triangle. The circumcenter of a triangle is the center of its circumcircle. All triangles have exactly one circumcircle and, therefore, exactly one circumcenter. A polygon is a geometric figure that lies in a plane and has a finite number of sides. A polygon that has a circumcircle is called a cyclic polygon. All triangles, rectangles and simple polygons with sides of equal length are cyclic.
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Instructions
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1
Label each vertex of a triangle A, B and C. Set the points of the compass so that the distance between them is greater than half the distance between points A and B. Inscribe a circle around point A. Inscribe a circle of equal radius around point B. These two circles will intersect at two points.
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2
Use a ruler to draw a line segment containing the two points of intersection for the circles drawn in step 1. This line segment lies on the perpendicular bisector of side AB.
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3
Set the points of the compass so that the distance between them is greater than half the distance between points B and C. Inscribe a circle around point B. Inscribe a circle of equal radius around point C. Use the ruler to connect the points of intersection of the circles thus constructed. This line segment lies on the perpendicular bisector of side BC.
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4
Observe that the intersection of the perpendicular bisectors constructed in steps 2 and 3 is the circumcenter of the triangle. The perpendicular bisector of side AC may be constructed to verity that it also intersects the triangle's circumcenter.
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References
- Photo Credit Ball State University
